1. Field of the Invention
This invention relates to a method and apparatus for locating the source of an unknown signal received by a plurality of signal relays.
2. Discussion of Prior Art
In IEEE Trans. on Aerospace and Electronic Systems, Vol. AES-18, No. 2, March 1982, P C Chestnut describes the basic technique of locating the source of an unknown signal such as a ground-based communications antenna; it involves determining the time difference of arrival (TDOA) and/or frequency difference of arrival (FDOA) of two signals from the source relayed to receivers by respective intercept platforms in the form of relay satellites in geostationary or geosynchronous orbits. The signals are relayed by the satellites along two independent signal paths to a receiving station, ie ground-satellite-ground paths. One satellite lies in the main beam or lobe of the source antenna radiation pattern and the other in a sidelobe. Each satellite accepts a signal (uplink) from the source, frequency shifts it using a turnaround oscillator and returns its frequency-shifted equivalent (downlink) to a ground receiver. The two signal path lengths are normally unequal, and this gives two signal arrival times at the receiver differing by the TDOA value. FDOA is due to relay satellite motion relative to the Earth and to one another, which Doppler shifts both downlink signal frequencies. The positions of the two satellites and the receiving station are known, and the locus of points of constant TDOA or FDOA is in each case a surface which intercepts the Earth""s surface to define a curve referred to as a line of position (LOP). Two measurements of TDOA or FDOA at different times, or one of each at one or more times, provides two LOPs which intersect at the position of the source to be located.
TDOA is also referred to as differential time offset (DTO) and FDOA as differential frequency offset (DFO) or differential Doppler shift.
The technique of determining TDOA and FDOA from two received signals is described in IEEE Trans. on Acoustics Speech and Signal Processing, Vol. ASSP-29, No. 3, June 1981 by S Stein in a paper entitled xe2x80x9cAlgorithms for Correlation Function Processingxe2x80x9d. It is also described in U.S. Pat. No. 5,008,679 relating to a transmitter location system incorporating two relay satellites and using both TDOA and FDOA measurements. The technique involves deriving the degree of correlation between the signals by multiplying them together and integrating their product. Trial relative time shifts and frequency offsets are introduced in sequence between the signals and their correlation is determined for each. The time shift and frequency offset which maximise the correlation are taken to be the required TDOA and FDOA, subject to correction for signal propagation delays in satellite transponders and frequency shifts in satellites and in processing.
The degree of correlation is determined from what is referred to by Stein as the cross ambiguity function or CAF A(xcfx84,xcexd) defined by:                               A          ⁡                      (                          τ              ,              v                        )                          =                                            ∫              0                        τ                    ⁢                                                    z                1                *                            ⁡                              (                t                )                                      ⁢                                          z                2                            ⁡                              (                                  t                  +                  τ                                )                                      ⁢                          e                                                -                  2                                ⁢                π                ⁢                                  xe2x80x83                                ⁢                i                ⁢                                  xe2x80x83                                ⁢                v                ⁢                                  xe2x80x83                                ⁢                t                                      ⁢                          ⅆ              t                                                          (        1        )            
A(xcfx84,xcexd) is the integral of the product of two signals z1(t) and z2(t) [complex or analytic versions of real signals s1(t) and s2(t)] after a trial time shift xcfx84 and a trial frequency shift xcexd have been introduced between them in processing after reception at the receiving station. The asterisk in z1*(t) indicates a complex conjugate. When a maximum value of the modulus of A(xcfx84,xcexd), ie |A(xcfx84,xcexd)|, is obtained, this being a correlation peak in the surface |A(xcfx84,xcexd)| as a function of the two variables xcfx84 and xcexd, the values of xcfx84 and xcexd for the peak are the required TDOA and FDOA.
The system of U.S. Pat. No. 5,008,679 requires satellite positions and velocities to be known accurately, and needs highly stable phase in ground station and satellite oscillators. It has bandwidth limitations for satellite orbits inclined to the Earth""s equatorial plane, and needs two receivers which are on the same site and have common time and frequency references.
U.S. Pat. No. 6,018,312 to Haworth relates to a transmitter location system employing a reference signal passing via the same satellite relays as the unknown signal and processed in phase coherence with it. The reference signal is used to remove a number of sources of error and limitations to which earlier techniques are subject, giving improved accuracy and capability for use under a wider range of conditions. Despite this improvement it has been found surprisingly that from time to time it can be impossible to discern a correlation peak in the CAF surface |A(xcfx84,xcexd)|-all that can be seen is noise.
A related but different technique for counteracting sources of error using a broad band approach is disclosed in U.S. Pat. No. 5,594,452 to Webber et al.
It is an object of this invention to provide an alternative method and apparatus for transmitter location.
The present invention provides a method of locating the source of an unknown signal received by a plurality of signal relays, the method including the steps of:
(a) arranging for a plurality of receivers to receive replicas of the unknown signal via respective signal relays; and
(b) subjecting the replicas to correlation processing;
characterised in that correlation processing in step (b) is performed with a complex correlation function (CCF) at least partly compensated for change in the replicas"" Differential Frequency Offset (DFO) with time due to relay motion relative to the source and receivers.
In a preferred embodiment of the invention, correlation processing in step (b) is also performed with data sets adapted in phase and subject to data replication or removal to counteract time dilation arising from relay motion relative to the source and receivers.
As indicated above it has been found that the reason for failure to obtain a correlation peak using a prior art ambiguity function is due to relay motion relative to the source and receivers. This is very surprising for geostationary satellite relays in particular, because their motion has hitherto been treated as constant over a measurement interval, which in turn implies that it affects all measurements at a site equally. Satellite motion alone would not have been expected to make a correlation peak obtainable on some occasions but not others. Despite this, in accordance with the invention it has been discovered that signal correlation is affected by velocity and acceleration components of the relay satellite along the lines joining it to the source and receiver, which results in the replicas"" DFO and Differential Time Offset (DTO) being time dependent. DFO variation can be compensated as indicated above by adapting the correlation function, and where necessary DTO variation can be compensated also by adapting data samples.
Correlation processing in step (b) may include introducing a trial time offset between the replicas and evaluating their correlation and iterating this to obtain a correlation maximum and derive at least one of the replicas"" DTO and DFO; it may be carried out with a CCF containing an exponent of a function of time having a first term which is a constant DFO value and a second term which is a product of time and a constant value for rate of change of DFO with time, ie a constant differential frequency rate offset (DFRO) value, and wherein step (b) also includes introducing a trial value corresponding to DFRO prior to evaluating correlation and iterating one type of trial value for each of the other type, repeating for more values of the other type and determining a DFRO value appropriate to compensate at least partly for change in DFO with time.
The CCF may be expressed as A(xcfx840, b1, b2) given by:                               A          ⁡                      (                                          τ                0                            ,                              b                1                            ,                              b                2                                      )                          =                                            ∫              0                        τ                    ⁢                                                    z                1                *                            ⁡                              (                t                )                                      ⁢                          z              ⁡                              (                                  t                  +                                      τ                    0                                                  )                                      ⁢                          e                                                -                  2                                ⁢                π                ⁢                                  xe2x80x83                                ⁢                                  i                  ⁡                                      (                                                                  b                        1                                            +                                              2                        ⁢                                                  b                          2                                                ⁢                        t                                                              )                                                  ⁢                t                                      ⁢                          ⅆ              t                                                          (        2        )            
where z1 and z2 are data sets representing two signals being correlated after traversing different paths, the asterisk denoting the complex conjugate of z1, T is a time over which data sets are taken, xcfx840 is the signals"" DTO, and b1 and b2 are constants in a linear approximation to the variation of their DFO with time t as follows:
DFOxe2x89xa1xcexd=b1+2b2txe2x80x83xe2x80x83(3)
where b1 is an initial constant DFO value at initiation of data recordal and 2b2 is DFRO as defined above.
The constant DFO value b1 may be determined by Fourier transformation of the Equation (2) product of z1*(t)z2(t+xcfx840)exp(xe2x88x922xcfx80ib2t2) to the frequency domain (ie ignoring the b1 term) after each iteration of Step (b), b1 being subsequently determined as the frequency at which the CCF maximum occurs. This reduces the computation required because it avoids stepping through trial values of b1 and re-evaluating the CCF for each. For a data set of N samples it reduces the number of computations from of order N2 to N logeN, a substantial reduction for large Nxcx9c106.
Correlation may be performed with a sample data set adapted in phase and number of samples, samples being replicated in or removed from the set according which data set is selected for adaptation (z1 or z2) and also to the sign of the rate of change with time of DTO associated with the data set. Data samples in one of two data sets to be correlated may adapted in phase by samples following a removed sample being multiplied by a phase factor or by samples including and following a replicated sample being multiplied by such a factor, the phase factor being either e2xcfx80ifxcex94t or exe2x88x922xcfx80ifxcex94t according to which of the two data sets is adapted and to the sign of DTO change with time, and wherein f is a signal band centre frequency of the samples after downconversion for sampling and xcex94t is the interval between samples.
Samples may alternatively be selected for removal and replication on the basis of the following equation:                               τ          m                =                                                            -                                  λ                  c                                            ⁢                              b                1                xe2x80x2                            ⁢                              t                m                                      -                                          λ                c                            ⁢                              b                2                            ⁢                              t                m                2                                              =                      m            ⁢                          xe2x80x83                        ⁢            Δ            ⁢                          xe2x80x83                        ⁢            t                                              (        4        )            
where tm is the time from initiation of sampling to the mth sample selected for alteration, m is the selection number, xcex94t is the sampling interval, xcfx84m is the time dilation (expressed as a number of sampling intervals) and xcex is the wavelength at the centre frequency of the signal sampling band before any frequency downconversion at a receiving site. The parameter bxe2x80x21 is an estimate of DFO (b1) with any systematic error (eg frequency shift at a satellite relay) counteracted by deriving an estimated correction using a reference signal. The parameter bxe2x80x21 may alternatively be derived by using trial values of it and calculating the modulus of the CCF until a CCF maximum is obtained. It also is possible to exploit b2 in the above expression as an independent parameter, thereby dissociating time dilation and time variation of DFO. Equation (4) is solved for tm to determine times at which time dilation results in data sets z1 and z2 being out of step by successive increments of xcex94t. If the effects of time dilation are not too severe, a linear approximation may be employed by deleting the tm2 term in Equation (4).
In an alternative aspect, the present invention provides a location device for locating the source of an unknown signal received by a plurality of signal relays, and including:
(a) a plurality of receivers for receiving replicas of the unknown signal via respective signal relays;
(b) a correlation processor for correlating the replicas and obtaining a correlation maximum indicating at least one of their DTO and DFO;
characterised in that the correlation processor is arranged to perform correlation with a complex correlation function (CCF) at least partly compensated for change in DFO with time due to relay motion relative to the source and receivers.
In a preferred embodiment of the invention, the correlation processor is also arranged to perform correlation with data sets adapted in phase and subject to data replication or removal to counteract time dilation arising from relay motion relative to the source and receivers.
The correlation processor may be arranged to employ a CCF containing an exponent of a function of time having a first term which is a constant DFO value and a second term which is a product of time and a constant value for rate of change of DFO with time, ie a constant differential frequency rate offset (DFRO) value, and wherein the correlation processor is also arranged to introduce trial values of DFRO and to evaluate correlation for pairs of trial values of DTO and DFRO iteratively to obtain a correlation maximum.
The correlation processor may be arranged to introduce a trial time offset between the replicas, evaluate their correlation and iterate this procedure to obtain a correlation maximum. It may employ a sample data set adapted in phase and number of samples, samples being replicated in or removed from the set according which data set is selected for adaptation (z1or z2) and also to the sign of the rate of change with time of DTO associated with the data set. It may be arranged to adapt samples in one of two data sets to be correlated in phase by multiplying samples following a removed sample by a phase factor or by multiplying samples including and following a replicated sample by such a factor, the phase factor being either e2xcfx80ifxcex94t or exe2x88x922xcfx80ifxcex94t according to which of the two data sets is adapted and to the sign of DTO change with time, and wherein f is a signal band centre frequency of the samples after downconversion for sampling and xcex94t is the interval between samples.
The correlation processor may select samples for removal and replication on the basis of the correlation function""s time dimension spread over an interval in which the samples were obtained. If a CCF peak is obtainable from data without time dilation compensation, the time over which correlation extends may be estimated. A selected data set may be contracted or expanded by the removal or insertion of samples according to whether data set z1 or z2 is adjusted and also according to whether time dilation is positive or negative. Alternatively, the correlation processor may select samples for removal and replication on the basis of Equation (4) above or a linear approximation thereto